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basically done but to long

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@ -323,11 +323,11 @@ labelformat=brace, position=top]{subcaption}
\begin{block}{}
\begin{equation}
\label{eq:one_qubit_model}
H = \frac{1}{2} σ_z + \frac{1}{2} ∑_λ\qty(g_λ σ_x^† a_λ + g_λ^\ast
H = \frac{1}{2} σ_z + \frac{f(τ)}{2} ∑_λ\qty(g_λ σ_x^† a_λ + g_λ^\ast
σ_x a_λ^†) + ∑_λ ω_λ a_λ^\dag a_λ,\;\ket{ψ_{0}}_{\sys} = \ket{\downarrow}
\end{equation}
\begin{itemize}
\item \(L(τ) = \sin^2(\frac{Δ}{2} τ)σ_x\)
\item \(f(τ) = \sin^2(\frac{Δ}{2} τ)\)
\item initial state of total system: \(ρ_{0} = \ketbra{\downarrow}
\otimes \frac{\eu^{-β H_{\bath}}}{Z}\)
\item Shifted SD for resonance
@ -343,17 +343,28 @@ labelformat=brace, position=top]{subcaption}
\end{itemize}
\begin{figure}[h]
\centering
\only<1>{\includegraphics[height=.65\textheight]{figs/modcoup/omegas_total}}
\only<2>{\includegraphics[height=.65\textheight]{figs/modcoup/omega_energies_and_powers}}
\includegraphics[height=.65\textheight]{figs/modcoup/omegas_total}
\end{figure}
\note[item]{energy normalized to ergo}
\note[item]{vert lines bath memory time}
\end{frame}
\begin{frame}
\frametitle{Speed Limit}
\begin{figure}[h]
\centering
\includegraphics[height=.65\textheight]{figs/modcoup/power_en_heatmap}
\end{figure}
\end{frame}
\subsection{Otto Cycle}
\begin{frame}
\frametitle{Otto Cycle (proof of concept)}
\frametitle{Quantum Otto Cycle}
\begin{figure}
\centering
\input{figs/drawings/otto.pdf_tex}
\end{figure}
\begin{block}{Model}
Spin-Boson model with compression of \(H_{\sys}\) and modulation
of \(L\).
@ -361,109 +372,49 @@ labelformat=brace, position=top]{subcaption}
\begin{itemize}
\item classical toy model of the quantum heat engine community\footcite{Geva1992Feb}
\end{itemize}
\end{frame}
\begin{frame}
\frametitle{Modulation and Spectral Densities}
\begin{figure}[h]
\centering
\includegraphics{figs/otto/modulation}
\includegraphics{figs/otto/spectral_densities}
\end{figure}
\end{frame}
\begin{frame}
\begin{figure}[h]
\centering
\includegraphics{figs/otto/energy_cont}
\end{figure}
\end{frame}
\begin{frame}
\begin{frame}{Full Energy Overview}
\begin{figure}[h]
\centering
\includegraphics{figs/otto/energy_strobe}
\end{figure}
\end{frame}
\begin{frame}
\begin{frame}{Power Contributions}
\begin{figure}[h]
\centering
\includegraphics{figs/otto/power}
\end{figure}
\begin{itemize}
\item \(\bar{P} = 1.98 \cdot 10^{-3} \pm 2.3 \cdot 10^{-5}\),
\(η\approx 20\%\), \(T_{c}=1\), \(T_{h}=20\)
\item \(\bar{P} = .0025\),
\(η\approx 29\%\), \(T_{c}=1\), \(T_{h}=20\)
\item no tuning of parameters, except for resonant coupling
\item long bath memory \(ω_{c}=1\), but weak-ish coupling
\end{itemize}
\end{frame}
\begin{frame}{Questions (for the future)}
\begin{itemize}
\item better performance through ``overlapping'' phases?
\item strong coupling any good?
\item non-Markovianity + strong coupling any good?
\item what is the optimal efficiency and power? (probably no
advantage here)
\end{itemize}
\end{frame}
\subsection{Anti-Zeno Engine}
\begin{frame}
\frametitle{Anti-Zeno Engine}
\begin{block}{Question}
Is there a use for non-Markovianity in quantum heat engines?
\end{block}
\begin{itemize}
\item \cite{Mukherjee2020Jan} claims that one can exploit the
time-energy uncertainty for quantum advantage\footnote{I'd be
careful to call this quantum advantage.}
\end{itemize}
\begin{block}{Model}
Qubit coupled to two baths of different
temperatures (\(T_c, T_h\))
\begin{equation}
\label{eq:antizenomodel}
H_\sys= \frac12 \qty[ω_0 + γ Δ\sin(Δ t)]σ_z,\, L_{c,h}=\frac12 σ_x
\end{equation}
\note[item]{frictionless dynamics}
\end{block}
\end{frame}
\begin{frame}
\begin{figure}[h]
\centering
\includegraphics{figs/anti_zeno/with_gap_coupling_diagram}
\end{figure}
\begin{itemize}
\item couple for \(n\) modulation periods slightly of resonance
\item for smaller \(n\) the \(\sin((ω-(ω_{0}\pm Δ))τ)/((ω-(ω_{0}\pm
Δ)) τ)\) has a greater overlap
\(\implies\) controls power output
\end{itemize}
\end{frame}
\begin{frame}
\begin{frame}{Continuously Coupled Version}
\begin{figure}
\centering
\begin{subfigure}[t]{.49\linewidth}
\centering
\includegraphics[width=\linewidth]{anti_zeno/anti_zeno_without_cool}
\caption{\tval{anti_zeno/power_without_cool}}
\end{subfigure}
\begin{subfigure}[t]{.49\linewidth}
\centering
\includegraphics[width=\linewidth]{anti_zeno/anti_zeno_with_cool}
\caption{
\tval{anti_zeno/power_with_cool}}
\end{subfigure}
\includegraphics{figs/otto/energy_strobe_continuous}
\end{figure}
\begin{exampleblock}{Parameters}
{\tval{anti_zeno/delta}, \tval{anti_zeno/gamma}, \tval{anti_zeno/omega_alpha},
\tval{anti_zeno/omega_zero}, \tval{anti_zeno/tc}, \tval{anti_zeno/th}}
\end{exampleblock}
\end{frame}
\begin{frame}{Current Work}
\begin{itemize}
\item this is not properly converged yet \(\rightarrow\) newer
results: no advantage at these temperatures / coupling strengths
\item new simulations with temperatures from paper
(\(β_{h(c)}=0.0005(0.005)\)) are promising
\begin{itemize}
\item interesting \(\rightarrow\) no good steady state power in this case
(insufficient samples?)
\end{itemize}
\item better performance through ``overlapping'' and shifting strokes?
\item stronger coupling any good?
\item non-Markovianity + strong coupling any good?
\item what is the optimal efficiency and power?
\end{itemize}
\end{frame}

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